No, you do not need CRT, look at what PaulRS did. If you have , , .... , so that whenever then where . This is not CRT, just property of relative primeness. CRT only enters when the 's are different for each modolus.

March 30th 2008, 09:44 AM

Moo

Oh, i didn't know this thing :-) d'you have a wiki link ?

Why that :

Quote:

THus: a^{60}\equiv{1}(\bmod{1001}) if a is coprime to 1001

?

Thanks !

March 30th 2008, 10:01 AM

ThePerfectHacker

Quote:

Originally Posted by Moo

Oh, i didn't know this thing :-) d'you have a wiki link ?

Why that :

Quote:

Originally Posted by Paul

THus: a^{60}\equiv{1}(\bmod{1001}) if a is coprime to 1001

?

Thanks !

(Assuming is such that ).

Because, .

Then,.

Thus..

Quote:

Originally Posted by Moo

This is the problem... You have to show it for any integer, not coprime oO

(What does oO mean?)

But it will not work for any integer. Say then (I just did it on my calculator (Tongueout) ).

March 30th 2008, 10:18 AM

Moo

oO is a smiley :D

That's the problem, the initial text said that it was for any integer... I couldn't verify with my calculator, thanks

Quote:

Thus..

This implication seems odd to me. I don't see with which theorem/property we can say it (although i agree with the result :p)

March 30th 2008, 11:01 AM

ThePerfectHacker

Quote:

Originally Posted by Moo

This implication seems odd to me. I don't see with which theorem/property we can say it (although i agree with the result :p)